Fixed moer tyops

[ghc.git] / compiler / typecheck / TcSimplify.lhs

\begin{code}
{-# OPTIONS -fno-warn-tabs #-}
-- The above warning supression flag is a temporary kludge.
-- While working on this module you are encouraged to remove it and
-- detab the module (please do the detabbing in a separate patch). See
--     http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#TabsvsSpaces
-- for details

module TcSimplify( 
       simplifyInfer, quantifyPred,
       simplifyAmbiguityCheck,
       simplifyDefault, 
       simplifyRule, simplifyTop, simplifyInteractive,
       solveWantedsTcM
  ) where

#include "HsVersions.h"

import TcRnTypes
import TcRnMonad
import TcErrors
import TcMType as TcM
import TcType 
import TcSMonad as TcS
import TcInteract 
import Inst
import FunDeps  ( growThetaTyVars )
import Type     ( classifyPredType, PredTree(..), getClassPredTys_maybe )
import Class    ( Class )
import Var
import Unique
import VarSet
import VarEnv 
import TcEvidence
import Name
import Bag
import ListSetOps
import Util
import PrelInfo
import PrelNames
import Class            ( classKey )
import BasicTypes       ( RuleName )
import Outputable
import FastString
import TrieMap () -- DV: for now
\end{code}


*********************************************************************************
*                                                                               * 
*                           External interface                                  *
*                                                                               *
*********************************************************************************

\begin{code}
simplifyTop :: WantedConstraints -> TcM (Bag EvBind)
-- Simplify top-level constraints
-- Usually these will be implications,
-- but when there is nothing to quantify we don't wrap
-- in a degenerate implication, so we do that here instead
simplifyTop wanteds
  = do { traceTc "simplifyTop {" $ text "wanted = " <+> ppr wanteds 
       ; ev_binds_var <- newTcEvBinds
       ; zonked_final_wc <- solveWantedsTcMWithEvBinds ev_binds_var wanteds simpl_top
       ; binds1 <- TcRnMonad.getTcEvBinds ev_binds_var
       ; traceTc "End simplifyTop }" empty

       ; traceTc "reportUnsolved {" empty
       ; binds2 <- reportUnsolved zonked_final_wc
       ; traceTc "reportUnsolved }" empty
         
       ; return (binds1 `unionBags` binds2) }

  where
    -- See Note [Top-level Defaulting Plan]
    simpl_top :: WantedConstraints -> TcS WantedConstraints
    simpl_top wanteds
      = do { wc_first_go <- nestTcS (solve_wanteds_and_drop wanteds)
           ; free_tvs <- TcS.zonkTyVarsAndFV (tyVarsOfWC wc_first_go) 
           ; let meta_tvs = filterVarSet isMetaTyVar free_tvs
                   -- zonkTyVarsAndFV: the wc_first_go is not yet zonked
                   -- filter isMetaTyVar: we might have runtime-skolems in GHCi, 
                   -- and we definitely don't want to try to assign to those!

           ; mapM_ defaultTyVar (varSetElems meta_tvs)   -- Has unification side effects
           ; simpl_top_loop wc_first_go }
    
    simpl_top_loop wc
      | isEmptyWC wc || insolubleWC wc
             -- Don't do type-class defaulting if there are insolubles
             -- Doing so is not going to solve the insolubles
      = return wc
      | otherwise
      = do { wc_residual <- nestTcS (solve_wanteds_and_drop wc)
           ; let wc_flat_approximate = approximateWC wc_residual
           ; something_happened <- applyDefaultingRules wc_flat_approximate
                                        -- See Note [Top-level Defaulting Plan]
           ; if something_happened then 
               simpl_top_loop wc_residual 
             else 
               return wc_residual }
\end{code}

Note [Top-level Defaulting Plan]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We have considered two design choices for where/when to apply defaulting.   
   (i) Do it in SimplCheck mode only /whenever/ you try to solve some 
       flat constraints, maybe deep inside the context of implications.
       This used to be the case in GHC 7.4.1.
   (ii) Do it in a tight loop at simplifyTop, once all other constraint has 
        finished. This is the current story.

Option (i) had many disadvantages: 
   a) First it was deep inside the actual solver, 
   b) Second it was dependent on the context (Infer a type signature, 
      or Check a type signature, or Interactive) since we did not want 
      to always start defaulting when inferring (though there is an exception to  
      this see Note [Default while Inferring])
   c) It plainly did not work. Consider typecheck/should_compile/DfltProb2.hs:
          f :: Int -> Bool
          f x = const True (\y -> let w :: a -> a
                                      w a = const a (y+1)
                                  in w y)
      We will get an implication constraint (for beta the type of y):
               [untch=beta] forall a. 0 => Num beta
      which we really cannot default /while solving/ the implication, since beta is
      untouchable.

Instead our new defaulting story is to pull defaulting out of the solver loop and
go with option (i), implemented at SimplifyTop. Namely:
     - First have a go at solving the residual constraint of the whole program
     - Try to approximate it with a flat constraint
     - Figure out derived defaulting equations for that flat constraint
     - Go round the loop again if you did manage to get some equations

Now, that has to do with class defaulting. However there exists type variable /kind/
defaulting. Again this is done at the top-level and the plan is:
     - At the top-level, once you had a go at solving the constraint, do 
       figure out /all/ the touchable unification variables of the wanted constraints.
     - Apply defaulting to their kinds

More details in Note [DefaultTyVar].

\begin{code}

------------------
simplifyAmbiguityCheck :: Name -> WantedConstraints -> TcM (Bag EvBind)
simplifyAmbiguityCheck name wanteds
  = traceTc "simplifyAmbiguityCheck" (text "name =" <+> ppr name) >> 
    simplifyTop wanteds  -- NB: must be simplifyTop so that we
                         --     do ambiguity resolution.  
                         -- See Note [Impedence matching] in TcBinds.
 
------------------
simplifyInteractive :: WantedConstraints -> TcM (Bag EvBind)
simplifyInteractive wanteds 
  = traceTc "simplifyInteractive" empty >>
    simplifyTop wanteds 

------------------
simplifyDefault :: ThetaType    -- Wanted; has no type variables in it
                -> TcM ()       -- Succeeds iff the constraint is soluble
simplifyDefault theta
  = do { traceTc "simplifyInteractive" empty
       ; wanted <- newFlatWanteds DefaultOrigin theta
       ; (unsolved, _binds) <- solveWantedsTcM (mkFlatWC wanted)

       ; traceTc "reportUnsolved {" empty
       -- See Note [Deferring coercion errors to runtime]
       ; reportAllUnsolved unsolved 
         -- Postcondition of solveWantedsTcM is that returned
         -- constraints are zonked. So Precondition of reportUnsolved
         -- is true.
       ; traceTc "reportUnsolved }" empty

       ; return () }
\end{code}


*********************************************************************************
*                                                                                 * 
*                            Inference
*                                                                                 *
***********************************************************************************

Note [Which variables to quantify]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Suppose the inferred type of a function is
   T kappa (alpha:kappa) -> Int
where alpha is a type unification variable and 
      kappa is a kind unification variable
Then we want to quantify over *both* alpha and kappa.  But notice that
kappa appears "at top level" of the type, as well as inside the kind
of alpha.  So it should be fine to just look for the "top level"
kind/type variables of the type, without looking transitively into the
kinds of those type variables.

\begin{code}
simplifyInfer :: Bool
              -> Bool                  -- Apply monomorphism restriction
              -> [(Name, TcTauType)]   -- Variables to be generalised,
                                       -- and their tau-types
              -> WantedConstraints
              -> TcM ([TcTyVar],    -- Quantify over these type variables
                      [EvVar],      -- ... and these constraints
                      Bool,         -- The monomorphism restriction did something
                                    --   so the results type is not as general as
                                    --   it could be
                      TcEvBinds)    -- ... binding these evidence variables
simplifyInfer _top_lvl apply_mr name_taus wanteds
  | isEmptyWC wanteds
  = do { gbl_tvs     <- tcGetGlobalTyVars            -- Already zonked
       ; zonked_taus <- zonkTcTypes (map snd name_taus)
       ; let tvs_to_quantify = varSetElems (tyVarsOfTypes zonked_taus `minusVarSet` gbl_tvs)
                               -- tvs_to_quantify can contain both kind and type vars
                               -- See Note [Which variables to quantify]
       ; qtvs <- zonkQuantifiedTyVars tvs_to_quantify
       ; return (qtvs, [], False, emptyTcEvBinds) }

  | otherwise
  = do { traceTc "simplifyInfer {"  $ vcat
             [ ptext (sLit "binds =") <+> ppr name_taus
             , ptext (sLit "closed =") <+> ppr _top_lvl
             , ptext (sLit "apply_mr =") <+> ppr apply_mr
             , ptext (sLit "(unzonked) wanted =") <+> ppr wanteds
             ]

              -- Historical note: Before step 2 we used to have a
              -- HORRIBLE HACK described in Note [Avoid unecessary
              -- constraint simplification] but, as described in Trac
              -- #4361, we have taken in out now.  That's why we start
              -- with step 2!

              -- Step 2) First try full-blown solving 

              -- NB: we must gather up all the bindings from doing
              -- this solving; hence (runTcSWithEvBinds ev_binds_var).
              -- And note that since there are nested implications,
              -- calling solveWanteds will side-effect their evidence
              -- bindings, so we can't just revert to the input
              -- constraint.

       ; ev_binds_var <- newTcEvBinds
       ; wanted_transformed <- solveWantedsTcMWithEvBinds ev_binds_var wanteds $
                               solve_wanteds_and_drop
                               -- Post: wanted_transformed are zonked

              -- Step 4) Candidates for quantification are an approximation of wanted_transformed
              -- NB: Already the fixpoint of any unifications that may have happened                                
              -- NB: We do not do any defaulting when inferring a type, this can lead
              -- to less polymorphic types, see Note [Default while Inferring]
 
              -- Step 5) Minimize the quantification candidates                             
              -- Step 6) Final candidates for quantification                
              -- We discard bindings, insolubles etc, because all we are
              -- care aout it

       ; tc_lcl_env <- TcRnMonad.getLclEnv
       ; let untch = tcl_untch tc_lcl_env
       ; quant_pred_candidates   
           <- if insolubleWC wanted_transformed 
              then return []   -- See Note [Quantification with errors]
              else do { gbl_tvs <- tcGetGlobalTyVars
                      ; let quant_cand = approximateWC wanted_transformed
                            meta_tvs   = filter isMetaTyVar (varSetElems (tyVarsOfCts quant_cand)) 
                      ; ((flats, _insols), _extra_binds) <- runTcS $ 
                        do { mapM_ (promoteAndDefaultTyVar untch gbl_tvs) meta_tvs
                                 -- See Note [Promote _and_ default when inferring]
                           ; _implics <- solveInteract quant_cand
                           ; getInertUnsolved }
                      ; return (map ctPred $ filter isWantedCt (bagToList flats)) }
                   -- NB: Dimitrios is slightly worried that we will get
                   -- family equalities (F Int ~ alpha) in the quantification
                   -- candidates, as we have performed no further unflattening
                   -- at this point. Nothing bad, but inferred contexts might
                   -- look complicated.

       -- NB: quant_pred_candidates is already the fixpoint of any 
       --     unifications that may have happened
       ; gbl_tvs        <- tcGetGlobalTyVars
       ; zonked_tau_tvs <- TcM.zonkTyVarsAndFV (tyVarsOfTypes (map snd name_taus))
       ; let init_tvs  = zonked_tau_tvs `minusVarSet` gbl_tvs
             poly_qtvs = growThetaTyVars quant_pred_candidates init_tvs 
                         `minusVarSet` gbl_tvs
             pbound    = filter (quantifyPred poly_qtvs) quant_pred_candidates
             
             -- Monomorphism restriction
             mr_qtvs         = init_tvs `minusVarSet` constrained_tvs
             constrained_tvs = tyVarsOfTypes quant_pred_candidates
             mr_bites        = apply_mr && not (null pbound)

             (qtvs, bound) | mr_bites  = (mr_qtvs,   [])
                           | otherwise = (poly_qtvs, pbound)
             
       ; traceTc "simplifyWithApprox" $
         vcat [ ptext (sLit "quant_pred_candidates =") <+> ppr quant_pred_candidates
              , ptext (sLit "gbl_tvs=") <+> ppr gbl_tvs
              , ptext (sLit "zonked_tau_tvs=") <+> ppr zonked_tau_tvs
              , ptext (sLit "pbound =") <+> ppr pbound
              , ptext (sLit "init_qtvs =") <+> ppr init_tvs 
              , ptext (sLit "poly_qtvs =") <+> ppr poly_qtvs ]

       ; if isEmptyVarSet qtvs && null bound
         then do { traceTc "} simplifyInfer/no quantification" empty                   
                 ; emitConstraints wanted_transformed
                    -- Includes insolubles (if -fdefer-type-errors)
                    -- as well as flats and implications
                 ; return ([], [], mr_bites, TcEvBinds ev_binds_var) }
         else do

       { traceTc "simplifyApprox" $ 
         ptext (sLit "bound are =") <+> ppr bound 
         
            -- Step 4, zonk quantified variables 
       ; let minimal_flat_preds = mkMinimalBySCs bound
             skol_info = InferSkol [ (name, mkSigmaTy [] minimal_flat_preds ty)
                                   | (name, ty) <- name_taus ]
                        -- Don't add the quantified variables here, because
                        -- they are also bound in ic_skols and we want them to be
                        -- tidied uniformly

       ; qtvs_to_return <- zonkQuantifiedTyVars (varSetElems qtvs)

            -- Step 7) Emit an implication
       ; minimal_bound_ev_vars <- mapM TcM.newEvVar minimal_flat_preds
       ; let implic = Implic { ic_untch    = pushUntouchables untch
                             , ic_skols    = qtvs_to_return
                             , ic_fsks     = []  -- wanted_tansformed arose only from solveWanteds
                                                 -- hence no flatten-skolems (which come from givens)
                             , ic_given    = minimal_bound_ev_vars
                             , ic_wanted   = wanted_transformed 
                             , ic_insol    = False
                             , ic_binds    = ev_binds_var
                             , ic_info     = skol_info
                             , ic_env      = tc_lcl_env }
       ; emitImplication implic
         
       ; traceTc "} simplifyInfer/produced residual implication for quantification" $
             vcat [ ptext (sLit "implic =") <+> ppr implic
                       -- ic_skols, ic_given give rest of result
                  , ptext (sLit "qtvs =") <+> ppr qtvs_to_return
                  , ptext (sLit "spb =") <+> ppr quant_pred_candidates
                  , ptext (sLit "bound =") <+> ppr bound ]

       ; return ( qtvs_to_return, minimal_bound_ev_vars
                , mr_bites,  TcEvBinds ev_binds_var) } }

quantifyPred :: TyVarSet           -- Quantifying over these
             -> PredType -> Bool   -- True <=> quantify over this wanted
quantifyPred qtvs pred
  | isIPPred pred = True  -- Note [Inheriting implicit parameters]
  | otherwise     = tyVarsOfType pred `intersectsVarSet` qtvs
\end{code}

Note [Inheriting implicit parameters]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Consider this:

        f x = (x::Int) + ?y

where f is *not* a top-level binding.
From the RHS of f we'll get the constraint (?y::Int).
There are two types we might infer for f:

        f :: Int -> Int

(so we get ?y from the context of f's definition), or

        f :: (?y::Int) => Int -> Int

At first you might think the first was better, because then
?y behaves like a free variable of the definition, rather than
having to be passed at each call site.  But of course, the WHOLE
IDEA is that ?y should be passed at each call site (that's what
dynamic binding means) so we'd better infer the second.

BOTTOM LINE: when *inferring types* you must quantify over implicit
parameters, *even if* they don't mention the bound type variables.
Reason: because implicit parameters, uniquely, have local instance
declarations. See the predicate quantifyPred.

Note [Quantification with errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If we find that the RHS of the definition has some absolutely-insoluble
constraints, we abandon all attempts to find a context to quantify
over, and instead make the function fully-polymorphic in whatever
type we have found.  For two reasons
  a) Minimise downstream errors
  b) Avoid spurious errors from this function
   

Note [Default while Inferring]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Our current plan is that defaulting only happens at simplifyTop and
not simplifyInfer.  This may lead to some insoluble deferred constraints
Example:

instance D g => C g Int b 

constraint inferred = (forall b. 0 => C gamma alpha b) /\ Num alpha
type inferred       = gamma -> gamma 

Now, if we try to default (alpha := Int) we will be able to refine the implication to 
  (forall b. 0 => C gamma Int b) 
which can then be simplified further to 
  (forall b. 0 => D gamma)
Finally we /can/ approximate this implication with (D gamma) and infer the quantified
type:  forall g. D g => g -> g

Instead what will currently happen is that we will get a quantified type 
(forall g. g -> g) and an implication:
       forall g. 0 => (forall b. 0 => C g alpha b) /\ Num alpha

which, even if the simplifyTop defaults (alpha := Int) we will still be left with an 
unsolvable implication:
       forall g. 0 => (forall b. 0 => D g)

The concrete example would be: 
       h :: C g a s => g -> a -> ST s a
       f (x::gamma) = (\_ -> x) (runST (h x (undefined::alpha)) + 1)

But it is quite tedious to do defaulting and resolve the implication constraints and
we have not observed code breaking because of the lack of defaulting in inference so 
we don't do it for now.



Note [Minimize by Superclasses]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
When we quantify over a constraint, in simplifyInfer we need to
quantify over a constraint that is minimal in some sense: For
instance, if the final wanted constraint is (Eq alpha, Ord alpha),
we'd like to quantify over Ord alpha, because we can just get Eq alpha
from superclass selection from Ord alpha. This minimization is what
mkMinimalBySCs does. Then, simplifyInfer uses the minimal constraint
to check the original wanted.


Note [Avoid unecessary constraint simplification]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    -------- NB NB NB (Jun 12) ------------- 
    This note not longer applies; see the notes with Trac #4361.
    But I'm leaving it in here so we remember the issue.)
    ----------------------------------------
When inferring the type of a let-binding, with simplifyInfer,
try to avoid unnecessarily simplifying class constraints.
Doing so aids sharing, but it also helps with delicate 
situations like

   instance C t => C [t] where ..

   f :: C [t] => ....
   f x = let g y = ...(constraint C [t])... 
         in ...
When inferring a type for 'g', we don't want to apply the
instance decl, because then we can't satisfy (C t).  So we
just notice that g isn't quantified over 't' and partition
the constraints before simplifying.

This only half-works, but then let-generalisation only half-works.


*********************************************************************************
*                                                                                 * 
*                             RULES                                               *
*                                                                                 *
***********************************************************************************

See note [Simplifying RULE consraints] in TcRule

Note [RULE quanfification over equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Decideing which equalities to quantify over is tricky:
 * We do not want to quantify over insoluble equalities (Int ~ Bool)
    (a) because we prefer to report a LHS type error
    (b) because if such things end up in 'givens' we get a bogus
        "inaccessible code" error

 * But we do want to quantify over things like (a ~ F b), where
   F is a type function.

The difficulty is that it's hard to tell what is insoluble!
So we see whether the simplificaiotn step yielded any type errors,
and if so refrain from quantifying over *any* equalites.

\begin{code}
simplifyRule :: RuleName 
             -> WantedConstraints       -- Constraints from LHS
             -> WantedConstraints       -- Constraints from RHS
             -> TcM ([EvVar], WantedConstraints)   -- LHS evidence varaibles
-- See Note [Simplifying RULE constraints] in TcRule
simplifyRule name lhs_wanted rhs_wanted
  = do {         -- We allow ourselves to unify environment 
                 -- variables: runTcS runs with NoUntouchables
         (resid_wanted, _) <- solveWantedsTcM (lhs_wanted `andWC` rhs_wanted)
                              -- Post: these are zonked and unflattened

       ; zonked_lhs_flats <- zonkCts (wc_flat lhs_wanted)
       ; let (q_cts, non_q_cts) = partitionBag quantify_me zonked_lhs_flats
             quantify_me  -- Note [RULE quantification over equalities]
               | insolubleWC resid_wanted = quantify_insol
               | otherwise                = quantify_normal

             quantify_insol ct = not (isEqPred (ctPred ct))

             quantify_normal ct
               | EqPred t1 t2 <- classifyPredType (ctPred ct)
               = not (t1 `eqType` t2)
               | otherwise
               = True
             
       ; traceTc "simplifyRule" $
         vcat [ ptext (sLit "LHS of rule") <+> doubleQuotes (ftext name)
              , text "zonked_lhs_flats" <+> ppr zonked_lhs_flats 
              , text "q_cts"      <+> ppr q_cts
              , text "non_q_cts"  <+> ppr non_q_cts ]

       ; return ( map (ctEvId . ctEvidence) (bagToList q_cts)
                , lhs_wanted { wc_flat = non_q_cts }) }
\end{code}


*********************************************************************************
*                                                                                 * 
*                                 Main Simplifier                                 *
*                                                                                 *
***********************************************************************************

Note [Deferring coercion errors to runtime]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
While developing, sometimes it is desirable to allow compilation to succeed even
if there are type errors in the code. Consider the following case:

  module Main where

  a :: Int
  a = 'a'

  main = print "b"

Even though `a` is ill-typed, it is not used in the end, so if all that we're
interested in is `main` it is handy to be able to ignore the problems in `a`.

Since we treat type equalities as evidence, this is relatively simple. Whenever
we run into a type mismatch in TcUnify, we normally just emit an error. But it
is always safe to defer the mismatch to the main constraint solver. If we do
that, `a` will get transformed into

  co :: Int ~ Char
  co = ...

  a :: Int
  a = 'a' `cast` co

The constraint solver would realize that `co` is an insoluble constraint, and
emit an error with `reportUnsolved`. But we can also replace the right-hand side
of `co` with `error "Deferred type error: Int ~ Char"`. This allows the program
to compile, and it will run fine unless we evaluate `a`. This is what
`deferErrorsToRuntime` does.

It does this by keeping track of which errors correspond to which coercion
in TcErrors (with ErrEnv). TcErrors.reportTidyWanteds does not print the errors
and does not fail if -fdefer-type-errors is on, so that we can continue
compilation. The errors are turned into warnings in `reportUnsolved`.

Note [Zonk after solving]
~~~~~~~~~~~~~~~~~~~~~~~~~
We zonk the result immediately after constraint solving, for two reasons:

a) because zonkWC generates evidence, and this is the moment when we
   have a suitable evidence variable to hand.

Note that *after* solving the constraints are typically small, so the
overhead is not great.

\begin{code}
solveWantedsTcMWithEvBinds :: EvBindsVar
                           -> WantedConstraints
                           -> (WantedConstraints -> TcS WantedConstraints)
                           -> TcM WantedConstraints
-- Returns a *zonked* result
-- We zonk when we finish primarily to un-flatten out any
-- flatten-skolems etc introduced by canonicalisation of
-- types involving type funuctions.  Happily the result 
-- is typically much smaller than the input, indeed it is 
-- often empty.
solveWantedsTcMWithEvBinds ev_binds_var wc tcs_action
  = do { traceTc "solveWantedsTcMWithEvBinds" $ text "wanted=" <+> ppr wc
       ; wc2 <- runTcSWithEvBinds ev_binds_var (tcs_action wc)
       ; zonkWC ev_binds_var wc2 }
         -- See Note [Zonk after solving]

solveWantedsTcM :: WantedConstraints -> TcM (WantedConstraints, Bag EvBind)
-- Zonk the input constraints, and simplify them
-- Return the evidence binds in the BagEvBinds result
-- Discards all Derived stuff in result
-- Postcondition: fully zonked and unflattened constraints
solveWantedsTcM wanted 
  = do { ev_binds_var <- newTcEvBinds
       ; wanteds' <- solveWantedsTcMWithEvBinds ev_binds_var wanted solve_wanteds_and_drop
       ; binds <- TcRnMonad.getTcEvBinds ev_binds_var
       ; return (wanteds', binds) }

solve_wanteds_and_drop :: WantedConstraints -> TcS (WantedConstraints)
-- Since solve_wanteds returns the residual WantedConstraints,
-- it should alway be called within a runTcS or something similar,
solve_wanteds_and_drop wanted = do { wc <- solve_wanteds wanted 
                                   ; return (dropDerivedWC wc) }

solve_wanteds :: WantedConstraints -> TcS WantedConstraints 
-- so that the inert set doesn't mindlessly propagate.
-- NB: wc_flats may be wanted /or/ derived now
solve_wanteds wanted@(WC { wc_flat = flats, wc_impl = implics, wc_insol = insols }) 
  = do { traceTcS "solveWanteds {" (ppr wanted)

         -- Try the flat bit, including insolubles. Solving insolubles a 
         -- second time round is a bit of a waste; but the code is simple 
         -- and the program is wrong anyway, and we don't run the danger 
         -- of adding Derived insolubles twice; see 
         -- TcSMonad Note [Do not add duplicate derived insolubles] 
       ; traceTcS "solveFlats {" empty
       ; let all_flats = flats `unionBags` insols
       ; impls_from_flats <- solveInteract all_flats
       ; traceTcS "solveFlats end }" (ppr impls_from_flats)

       -- solve_wanteds iterates when it is able to float equalities 
       -- out of one or more of the implications. 
       ; unsolved_implics <- simpl_loop 1 (implics `unionBags` impls_from_flats)

       ; (unsolved_flats, insoluble_flats) <- getInertUnsolved

        -- We used to unflatten here but now we only do it once at top-level
        -- during zonking -- see Note [Unflattening while zonking] in TcMType
       ; let wc = WC { wc_flat  = unsolved_flats   
                     , wc_impl  = unsolved_implics 
                     , wc_insol = insoluble_flats }
                  
       ; bb <- getTcEvBindsMap
       ; tb <- getTcSTyBindsMap
       ; traceTcS "solveWanteds }" $
                 vcat [ text "unsolved_flats   =" <+> ppr unsolved_flats
                      , text "unsolved_implics =" <+> ppr unsolved_implics
                      , text "current evbinds  =" <+> ppr (evBindMapBinds bb)
                      , text "current tybinds  =" <+> vcat (map ppr (varEnvElts tb))
                      , text "final wc =" <+> ppr wc ]

       ; return wc }

simpl_loop :: Int
           -> Bag Implication
           -> TcS (Bag Implication)
simpl_loop n implics
  | n > 10 
  = traceTcS "solveWanteds: loop!" empty >> return implics
  | otherwise 
  = do { (floated_eqs, unsolved_implics) <- solveNestedImplications implics
       ; if isEmptyBag floated_eqs 
         then return unsolved_implics 
         else 
    do {   -- Put floated_eqs into the current inert set before looping
         impls_from_eqs <- solveInteract floated_eqs
       ; simpl_loop (n+1) (unsolved_implics `unionBags` impls_from_eqs)} }


solveNestedImplications :: Bag Implication
                        -> TcS (Cts, Bag Implication)
-- Precondition: the TcS inerts may contain unsolved flats which have 
-- to be converted to givens before we go inside a nested implication.
solveNestedImplications implics
  | isEmptyBag implics
  = return (emptyBag, emptyBag)
  | otherwise 
  = do { inerts <- getTcSInerts
       ; let thinner_inerts = prepareInertsForImplications inerts
                 -- See Note [Preparing inert set for implications]
  
       ; traceTcS "solveNestedImplications starting {" $ 
         vcat [ text "original inerts = " <+> ppr inerts
              , text "thinner_inerts  = " <+> ppr thinner_inerts ]
         
       ; (floated_eqs, unsolved_implics)
           <- flatMapBagPairM (solveImplication thinner_inerts) implics

       -- ... and we are back in the original TcS inerts 
       -- Notice that the original includes the _insoluble_flats so it was safe to ignore
       -- them in the beginning of this function.
       ; traceTcS "solveNestedImplications end }" $
                  vcat [ text "all floated_eqs ="  <+> ppr floated_eqs
                       , text "unsolved_implics =" <+> ppr unsolved_implics ]

       ; return (floated_eqs, unsolved_implics) }

solveImplication :: InertSet
                 -> Implication    -- Wanted
                 -> TcS (Cts,      -- All wanted or derived floated equalities: var = type
                         Bag Implication) -- Unsolved rest (always empty or singleton)
-- Precondition: The TcS monad contains an empty worklist and given-only inerts 
-- which after trying to solve this implication we must restore to their original value
solveImplication inerts
     imp@(Implic { ic_untch  = untch
                 , ic_binds  = ev_binds
                 , ic_skols  = skols 
                 , ic_fsks   = old_fsks
                 , ic_given  = givens
                 , ic_wanted = wanteds
                 , ic_info   = info
                 , ic_env    = env })
  = do { traceTcS "solveImplication {" (ppr imp) 

         -- Solve the nested constraints
         -- NB: 'inerts' has empty inert_fsks
       ; (new_fsks, residual_wanted) 
            <- nestImplicTcS ev_binds untch inerts $
               do { solveInteractGiven (mkGivenLoc info env) old_fsks givens 
                  ; residual_wanted <- solve_wanteds wanteds
                        -- solve_wanteds, *not* solve_wanteds_and_drop, because
                        -- we want to retain derived equalities so we can float
                        -- them out in floatEqualities
                  ; more_fsks <- getFlattenSkols
                  ; return (more_fsks ++ old_fsks, residual_wanted) }

       ; (floated_eqs, final_wanted)
             <- floatEqualities (skols ++ new_fsks) givens residual_wanted

       ; let res_implic | isEmptyWC final_wanted 
                        = emptyBag
                        | otherwise
                        = unitBag (imp { ic_fsks   = new_fsks
                                       , ic_wanted = dropDerivedWC final_wanted
                                       , ic_insol  = insolubleWC final_wanted })

       ; evbinds <- getTcEvBindsMap
       ; traceTcS "solveImplication end }" $ vcat
             [ text "floated_eqs =" <+> ppr floated_eqs
             , text "new_fsks =" <+> ppr new_fsks
             , text "res_implic =" <+> ppr res_implic
             , text "implication evbinds = " <+> ppr (evBindMapBinds evbinds) ]

       ; return (floated_eqs, res_implic) }
\end{code}


\begin{code}
floatEqualities :: [TcTyVar] -> [EvVar] -> WantedConstraints 
                -> TcS (Cts, WantedConstraints)
-- Post: The returned FlavoredEvVar's are only Wanted or Derived
-- and come from the input wanted ev vars or deriveds 
-- Also performs some unifications, adding to monadically-carried ty_binds
-- These will be used when processing floated_eqs later
floatEqualities skols can_given wanteds@(WC { wc_flat = flats })
  | hasEqualities can_given 
  = return (emptyBag, wanteds)   -- Note [Float Equalities out of Implications]
  | otherwise 
  = do { let (float_eqs, remaining_flats) = partitionBag is_floatable flats
       ; untch <- TcS.getUntouchables
       ; mapM_ (promoteTyVar untch) (varSetElems (tyVarsOfCts float_eqs))
             -- See Note [Promoting unification variables]
       ; ty_binds <- getTcSTyBindsMap
       ; traceTcS "floatEqualities" (vcat [ text "Flats =" <+> ppr flats
                                          , text "Floated eqs =" <+> ppr float_eqs
                                          , text "Ty binds =" <+> ppr ty_binds])
       ; return (float_eqs, wanteds { wc_flat = remaining_flats }) }
  where 
      -- See Note [Float equalities from under a skolem binding]
    skol_set = fixVarSet mk_next (mkVarSet skols)
    mk_next tvs = foldrBag grow_one tvs flats
    grow_one (CFunEqCan { cc_tyargs = xis, cc_rhs = rhs }) tvs
       | intersectsVarSet tvs (tyVarsOfTypes xis) 
       = tvs `unionVarSet` tyVarsOfType rhs
    grow_one _ tvs = tvs

    is_floatable :: Ct -> Bool
    is_floatable ct = isEqPred pred && skol_set `disjointVarSet` tyVarsOfType pred
       where
         pred = ctPred ct

promoteTyVar :: Untouchables -> TcTyVar  -> TcS ()
-- When we float a constraint out of an implication we must restore
-- invariant (MetaTvInv) in Note [Untouchable type variables] in TcType
-- See Note [Promoting unification variables]
promoteTyVar untch tv 
  | isFloatedTouchableMetaTyVar untch tv
  = do { cloned_tv <- TcS.cloneMetaTyVar tv
       ; let rhs_tv = setMetaTyVarUntouchables cloned_tv untch
       ; setWantedTyBind tv (mkTyVarTy rhs_tv) }
  | otherwise
  = return ()

promoteAndDefaultTyVar :: Untouchables -> TcTyVarSet -> TyVar -> TcS ()
-- See Note [Promote _and_ default when inferring]
promoteAndDefaultTyVar untch gbl_tvs tv
  = do { tv1 <- if tv `elemVarSet` gbl_tvs 
                then return tv
                else defaultTyVar tv
       ; promoteTyVar untch tv1 }

defaultTyVar :: TcTyVar -> TcS TcTyVar
-- Precondition: MetaTyVars only
-- See Note [DefaultTyVar]
defaultTyVar the_tv
  | not (k `eqKind` default_k)
  = do { tv' <- TcS.cloneMetaTyVar the_tv
       ; let new_tv = setTyVarKind tv' default_k
       ; traceTcS "defaultTyVar" (ppr the_tv <+> ppr new_tv)
       ; setWantedTyBind the_tv (mkTyVarTy new_tv)
       ; return new_tv }
             -- Why not directly derived_pred = mkTcEqPred k default_k?
             -- See Note [DefaultTyVar]
             -- We keep the same Untouchables on tv'

  | otherwise = return the_tv    -- The common case
  where
    k = tyVarKind the_tv
    default_k = defaultKind k

approximateWC :: WantedConstraints -> Cts
-- Postcondition: Wanted or Derived Cts 
approximateWC wc 
  = float_wc emptyVarSet wc
  where 
    float_wc :: TcTyVarSet -> WantedConstraints -> Cts
    float_wc skols (WC { wc_flat = flats, wc_impl = implics }) 
      = do_bag (float_flat skols)   flats  `unionBags` 
        do_bag (float_implic skols) implics
                                 
    float_implic :: TcTyVarSet -> Implication -> Cts
    float_implic skols imp
      | hasEqualities (ic_given imp)  -- Don't float out of equalities
      = emptyCts                      -- cf floatEqualities
      | otherwise                     -- See Note [approximateWC]
      = float_wc skols' (ic_wanted imp)
      where
        skols' = skols `extendVarSetList` ic_skols imp `extendVarSetList` ic_fsks imp
            
    float_flat :: TcTyVarSet -> Ct -> Cts
    float_flat skols ct
      | tyVarsOfCt ct `disjointVarSet` skols 
      = singleCt ct
      | otherwise = emptyCts
        
    do_bag :: (a -> Bag c) -> Bag a -> Bag c
    do_bag f = foldrBag (unionBags.f) emptyBag
\end{code}

Note [ApproximateWC]
~~~~~~~~~~~~~~~~~~~~
approximateWC takes a constraint, typically arising from the RHS of a
let-binding whose type we are *inferring*, and extracts from it some
*flat* constraints that we might plausibly abstract over.  Of course
the top-level flat constraints are plausible, but we also float constraints
out from inside, if the are not captured by skolems.

However we do *not* float anything out if the implication binds equality
constriants, because that defeats the OutsideIn story.  Consider
   data T a where
     TInt :: T Int
     MkT :: T a

   f TInt = 3::Int

We get the implication (a ~ Int => res ~ Int), where so far we've decided 
  f :: T a -> res
We don't want to float (res~Int) out because then we'll infer  
  f :: T a -> Int
which is only on of the possible types. (GHC 7.6 accidentally *did*
float out of such implications, which meant it would happily infer
non-principal types.)

Note [DefaultTyVar]
~~~~~~~~~~~~~~~~~~~
defaultTyVar is used on any un-instantiated meta type variables to
default the kind of OpenKind and ArgKind etc to *.  This is important 
to ensure that instance declarations match.  For example consider

     instance Show (a->b)
     foo x = show (\_ -> True)

Then we'll get a constraint (Show (p ->q)) where p has kind ArgKind,
and that won't match the typeKind (*) in the instance decl.  See tests
tc217 and tc175.

We look only at touchable type variables. No further constraints
are going to affect these type variables, so it's time to do it by
hand.  However we aren't ready to default them fully to () or
whatever, because the type-class defaulting rules have yet to run.

An important point is that if the type variable tv has kind k and the
default is default_k we do not simply generate [D] (k ~ default_k) because:

   (1) k may be ArgKind and default_k may be * so we will fail

   (2) We need to rewrite all occurrences of the tv to be a type
       variable with the right kind and we choose to do this by rewriting 
       the type variable /itself/ by a new variable which does have the 
       right kind.

Note [Promote _and_ default when inferring]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we are inferring a type, we simplify the constraint, and then use
approximateWC to produce a list of candidate constraints.  Then we MUST

  a) Promote any meta-tyvars that have been floated out by 
     approximateWC, to restore invariant (MetaTvInv) described in 
     Note [Untouchable type variables] in TcType.

  b) Default the kind of any meta-tyyvars that are not mentioned in
     in the environment.

To see (b), suppose the constraint is (C ((a :: OpenKind) -> Int)), and we
have an instance (C ((x:*) -> Int)).  The instance doesn't match -- but it
should!  If we don't solve the constraint, we'll stupidly quantify over 
(C (a->Int)) and, worse, in doing so zonkQuantifiedTyVar will quantify over
(b:*) instead of (a:OpenKind), which can lead to disaster; see Trac #7332.
Trac #7641 is a simpler example.

Note [Float Equalities out of Implications]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
For ordinary pattern matches (including existentials) we float 
equalities out of implications, for instance: 
     data T where 
       MkT :: Eq a => a -> T 
     f x y = case x of MkT _ -> (y::Int)
We get the implication constraint (x::T) (y::alpha): 
     forall a. [untouchable=alpha] Eq a => alpha ~ Int
We want to float out the equality into a scope where alpha is no
longer untouchable, to solve the implication!  

But we cannot float equalities out of implications whose givens may
yield or contain equalities:

      data T a where 
        T1 :: T Int
        T2 :: T Bool
        T3 :: T a 
        
      h :: T a -> a -> Int
      
      f x y = case x of 
                T1 -> y::Int
                T2 -> y::Bool
                T3 -> h x y

We generate constraint, for (x::T alpha) and (y :: beta): 
   [untouchables = beta] (alpha ~ Int => beta ~ Int)   -- From 1st branch
   [untouchables = beta] (alpha ~ Bool => beta ~ Bool) -- From 2nd branch
   (alpha ~ beta)                                      -- From 3rd branch 

If we float the equality (beta ~ Int) outside of the first implication and 
the equality (beta ~ Bool) out of the second we get an insoluble constraint.
But if we just leave them inside the implications we unify alpha := beta and
solve everything.

Principle: 
    We do not want to float equalities out which may need the given *evidence*
    to become soluble.

Consequence: classes with functional dependencies don't matter (since there is 
no evidence for a fundep equality), but equality superclasses do matter (since 
they carry evidence).

Note [Float equalities from under a skolem binding]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
You might worry about skolem escape with all this floating.
For example, consider
    [2] forall a. (a ~ F beta[2] delta, 
                   Maybe beta[2] ~ gamma[1])

The (Maybe beta ~ gamma) doesn't mention 'a', so we float it, and
solve with gamma := beta. But what if later delta:=Int, and 
  F b Int = b.  
Then we'd get a ~ beta[2], and solve to get beta:=a, and now the
skolem has escaped!

But it's ok: when we float (Maybe beta[2] ~ gamma[1]), we promote beta[2]
to beta[1], and that means the (a ~ beta[1]) will be stuck, as it should be.

Previously we tried to "grow" the skol_set with the constraints, to get
all the tyvars that could *conceivably* unify with the skolems, but that
was far too conservative (Trac #7804). Example: this should be fine:
    f :: (forall a. a -> Proxy x -> Proxy (F x)) -> Int
    f = error "Urk" :: (forall a. a -> Proxy x -> Proxy (F x)) -> Int

BUT (sigh) we have to be careful.  Here are some edge cases:

a)    [2]forall a. (F a delta[1] ~ beta[2],   delta[1] ~ Maybe beta[2])
b)    [2]forall a. (F b ty ~ beta[2],         G beta[2] ~ gamma[2])
c)    [2]forall a. (F a ty ~ beta[2],         delta[1] ~ Maybe beta[2])

In (a) we *must* float out the second equality, 
       else we can't solve at all (Trac #7804).

In (b) we *must not* float out the second equality.  
       It will ultimately be solved (by flattening) in situ, but if we
       float it we'll promote beta,gamma, and render the first equality insoluble.

In (c) it would be OK to float the second equality but better not to.
       If we flatten we see (delta[1] ~ Maybe (F a ty)), which is a 
       skolem-escape problem.  If we float the secodn equality we'll 
       end up with (F a ty ~ beta'[1]), which is a less explicable error.

Hence we start with the skolems, grow them by the CFunEqCans, and
float ones that don't mention the grown variables.  Seems very ad hoc.

Note [Promoting unification variables]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we float an equality out of an implication we must "promote" free
unification variables of the equality, in order to maintain Invariant
(MetaTvInv) from Note [Untouchable type variables] in TcType.  for the
leftover implication.

This is absolutely necessary. Consider the following example. We start
with two implications and a class with a functional dependency.

    class C x y | x -> y
    instance C [a] [a]
          
    (I1)      [untch=beta]forall b. 0 => F Int ~ [beta]
    (I2)      [untch=beta]forall c. 0 => F Int ~ [[alpha]] /\ C beta [c]

We float (F Int ~ [beta]) out of I1, and we float (F Int ~ [[alpha]]) out of I2. 
They may react to yield that (beta := [alpha]) which can then be pushed inwards 
the leftover of I2 to get (C [alpha] [a]) which, using the FunDep, will mean that
(alpha := a). In the end we will have the skolem 'b' escaping in the untouchable
beta! Concrete example is in indexed_types/should_fail/ExtraTcsUntch.hs:

    class C x y | x -> y where 
     op :: x -> y -> ()

    instance C [a] [a]

    type family F a :: *

    h :: F Int -> ()
    h = undefined

    data TEx where 
      TEx :: a -> TEx 


    f (x::beta) = 
        let g1 :: forall b. b -> ()
            g1 _ = h [x]
            g2 z = case z of TEx y -> (h [[undefined]], op x [y])
        in (g1 '3', g2 undefined)



Note [Solving Family Equations] 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
After we are done with simplification we may be left with constraints of the form:
     [Wanted] F xis ~ beta 
If 'beta' is a touchable unification variable not already bound in the TyBinds 
then we'd like to create a binding for it, effectively "defaulting" it to be 'F xis'.

When is it ok to do so? 
    1) 'beta' must not already be defaulted to something. Example: 

           [Wanted] F Int  ~ beta   <~ Will default [beta := F Int]
           [Wanted] F Char ~ beta   <~ Already defaulted, can't default again. We 
                                       have to report this as unsolved.

    2) However, we must still do an occurs check when defaulting (F xis ~ beta), to 
       set [beta := F xis] only if beta is not among the free variables of xis.

    3) Notice that 'beta' can't be bound in ty binds already because we rewrite RHS 
       of type family equations. See Inert Set invariants in TcInteract.

This solving is now happening during zonking, see Note [Unflattening while zonking]
in TcMType.


*********************************************************************************
*                                                                               * 
*                          Defaulting and disamgiguation                        *
*                                                                               *
*********************************************************************************

\begin{code}
applyDefaultingRules :: Cts -> TcS Bool
  -- True <=> I did some defaulting, reflected in ty_binds
                 
-- Return some extra derived equalities, which express the
-- type-class default choice. 
applyDefaultingRules wanteds
  | isEmptyBag wanteds 
  = return False
  | otherwise
  = do { traceTcS "applyDefaultingRules { " $ 
                  text "wanteds =" <+> ppr wanteds
                  
       ; info@(default_tys, _) <- getDefaultInfo
       ; let groups = findDefaultableGroups info wanteds
       ; traceTcS "findDefaultableGroups" $ vcat [ text "groups=" <+> ppr groups
                                                 , text "info=" <+> ppr info ]
       ; something_happeneds <- mapM (disambigGroup default_tys) groups

       ; traceTcS "applyDefaultingRules }" (ppr something_happeneds)

       ; return (or something_happeneds) }
\end{code}



\begin{code}
findDefaultableGroups 
    :: ( [Type]
       , (Bool,Bool) )  -- (Overloaded strings, extended default rules)
    -> Cts              -- Unsolved (wanted or derived)
    -> [[(Ct,Class,TcTyVar)]]
findDefaultableGroups (default_tys, (ovl_strings, extended_defaults)) wanteds
  | null default_tys             = []
  | otherwise = filter is_defaultable_group (equivClasses cmp_tv unaries)
  where 
    unaries     :: [(Ct, Class, TcTyVar)]  -- (C tv) constraints
    non_unaries :: [Ct]             -- and *other* constraints
    
    (unaries, non_unaries) = partitionWith find_unary (bagToList wanteds)
        -- Finds unary type-class constraints
    find_unary cc 
        | Just (cls,[ty]) <- getClassPredTys_maybe (ctPred cc)
        , Just tv <- tcGetTyVar_maybe ty
        , isMetaTyVar tv  -- We might have runtime-skolems in GHCi, and 
                          -- we definitely don't want to try to assign to those!
        = Left (cc, cls, tv)
    find_unary cc = Right cc  -- Non unary or non dictionary 

    bad_tvs :: TcTyVarSet  -- TyVars mentioned by non-unaries 
    bad_tvs = foldr (unionVarSet . tyVarsOfCt) emptyVarSet non_unaries 

    cmp_tv (_,_,tv1) (_,_,tv2) = tv1 `compare` tv2

    is_defaultable_group ds@((_,_,tv):_)
        = let b1 = isTyConableTyVar tv  -- Note [Avoiding spurious errors]
              b2 = not (tv `elemVarSet` bad_tvs)
              b4 = defaultable_classes [cls | (_,cls,_) <- ds]
          in (b1 && b2 && b4)
    is_defaultable_group [] = panic "defaultable_group"

    defaultable_classes clss 
        | extended_defaults = any isInteractiveClass clss
        | otherwise         = all is_std_class clss && (any is_num_class clss)

    -- In interactive mode, or with -XExtendedDefaultRules,
    -- we default Show a to Show () to avoid graututious errors on "show []"
    isInteractiveClass cls 
        = is_num_class cls || (classKey cls `elem` [showClassKey, eqClassKey, ordClassKey])

    is_num_class cls = isNumericClass cls || (ovl_strings && (cls `hasKey` isStringClassKey))
    -- is_num_class adds IsString to the standard numeric classes, 
    -- when -foverloaded-strings is enabled

    is_std_class cls = isStandardClass cls || (ovl_strings && (cls `hasKey` isStringClassKey))
    -- Similarly is_std_class

------------------------------
disambigGroup :: [Type]                  -- The default types 
              -> [(Ct, Class, TcTyVar)]  -- All classes of the form (C a)
                                         --  sharing same type variable
              -> TcS Bool   -- True <=> something happened, reflected in ty_binds

disambigGroup []  _grp
  = return False
disambigGroup (default_ty:default_tys) group
  = do { traceTcS "disambigGroup {" (ppr group $$ ppr default_ty)
       ; success <- tryTcS $ -- Why tryTcS? If this attempt fails, we want to 
                             -- discard all side effects from the attempt
                    do { setWantedTyBind the_tv default_ty
                       ; implics_from_defaulting <- solveInteract wanteds
                       ; MASSERT (isEmptyBag implics_from_defaulting)
                           -- I am not certain if any implications can be generated
                           -- but I am letting this fail aggressively if this ever happens.
                                     
                       ; checkAllSolved }

       ; if success then
             -- Success: record the type variable binding, and return
             do { setWantedTyBind the_tv default_ty
                ; wrapWarnTcS $ warnDefaulting wanteds default_ty
                ; traceTcS "disambigGroup succeeded }" (ppr default_ty)
                ; return True }
         else
             -- Failure: try with the next type
             do { traceTcS "disambigGroup failed, will try other default types }"
                           (ppr default_ty)
                ; disambigGroup default_tys group } }
  where
    ((_,_,the_tv):_) = group
    wanteds          = listToBag (map fstOf3 group)
\end{code}

Note [Avoiding spurious errors]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When doing the unification for defaulting, we check for skolem
type variables, and simply don't default them.  For example:
   f = (*)      -- Monomorphic
   g :: Num a => a -> a
   g x = f x x
Here, we get a complaint when checking the type signature for g,
that g isn't polymorphic enough; but then we get another one when
dealing with the (Num a) context arising from f's definition;
we try to unify a with Int (to default it), but find that it's
already been unified with the rigid variable from g's type sig